For each point in space, a microscope's resolving power is described by a function of three spatial variables called the point-spread function. The point-spread function is typically the Fourier Transform of an aperture distribution. Although the point-spread function is defined at all points in space, the region of most interest to microscopists is that region in which the point-spread function reaches its maximum value. This region is referred to as the "main lobe" of the point-spread function.
The overall shape of a point-spread function, and in particular the shape of the main lobe of a point-spread function, is determined by the microscope objective lens and the illumination source. The spatial location of the main lobe, however, is determined in part by the location of the lens in the three-dimensional space.
A point-spread function defines the resolution of a microscope because two luminous points in the field of view are resolvable only to the extent that their images can be separated by two main lobes from two different point-spread functions. Since the point-spread function is three dimensional, whether or not two luminous points are in separate main lobes depends on both how far apart they are and on the direction in which they are separated.
The transverse resolution of a microscope depends on the width of a cross section of the main lobe transverse to the optical axis. The images of two points in a plane transverse to the optical axis are resolvable if they are separated by a distance exceeding the width of the cross section. Similarly, the axial resolution of a microscope depends on the length of a cross section of the main lobe in a plane containing the optical axis. Images of two points in the plane containing the optical axis are resolvable to the extent they are separated by more than this length.
The point spread functions of the illuminating aperture and of the detecting aperture are formed by convolving the response of the lens to an infinitesimal point source (the lens's "impulse response") with a function representative of the spatial extent and intensity of the illumination source. In the ideal case, where the illumination source is an infinitesimal pinhole, the point-spread functions for both the illumination aperture and the detection aperture of a confocal microscope are sync functions in the axial direction and Bessel functions in the transverse direction. In the case of a pinhole having a finite aperture, the forms of the point spread functions are modified slightly as a result of the above-mentioned convolution.
While the forms of these functions depend on the geometry of the apertures and the spatial extent of the illuminating pinhole, the scales of these functions depend on the numerical apertures of the objective lenses. The axial extent of the main lobe is inversely proportional to the square of the numerical aperture whereas the transverse extent of the main lobe is inversely proportional to numerical aperture. Accordingly, the main lobe extends further in the axial direction than it does in the transverse direction. Because of this, the resolution in the axial direction is significantly poorer than the resolution in the transverse direction.
In conventional confocal microscopes, the overall point-spread function is the product of the point-spread functions for the illuminating aperture stop and for the detecting aperture stop. Since, as described above, these two point-spread functions are of the same form, the product of the two point-spread functions still has a main lobe which is long in the axial direction. The axial extent of the main lobe limits the axial resolution of the confocal microscope, thereby limiting the ability of the confocal microscope to perform optical sectioning on very thin layers.
Conventional methods of increasing axial resolution focus on using objective lenses with high numerical aperture. This is unattractive for several reasons. First, for applications requiring a wide field of view, the narrow field of a high numerical aperture lens is undesirable. Second, for certain applications such as the examination of images deep within tissue, the short focal length of a high numerical aperture lens makes it difficult to place the lens close enough to the region of interest for the microscope to function effectively. Third, for scanning which requires movement of the objective lens, the increased weight of a high numerical aperture lens limits the speed and precision with which the lens can be moved during scanning.
Accordingly, there exists a need for a confocal scanning microscope having enhanced axial resolution but without the constraints of short focal length, excessive weight and narrow field of view imposed by the use of a lens having a high numerical aperture.